Abstract
We study a class of biharmonic problems with Navier boundary condition and involving a generalized differential operator and competing nonlinearities with variable exponent. The main result of this paper establishes a sufficient condition for the existence of nontrivial weak solutions, in relationship with the values of a positive parameter. The proofs combine variational methods with analytic arguments. The approach developed in this paper allows the treatment of several classes of nonhomogeneous biharmonic problems with variable growth arising in applied sciences, including the capillarity equation and the mean curvature problem.